Munich Personal RePEc Archive

Conspicuous Consumption and

Within-Group Income Inequality

Li, Li and Mak, Eric and Pivovarova, Margarita

Shanghai University of Finance and Economics, Shanghai University

of Finance and Economics, Arizona State University

8 June 2016

Online at https://mpra.ub.uni-muenchen.de/83338/

MPRA Paper No. 83338, posted 28 Dec 2017 07:25 UTC

Conspicuous Consumption andWithin-Group Income Inequality

(Not for Public Circulation)

Li Li∗, Eric Mak†, Margarita Pivovarova‡

June 8, 2016§

Abstract

Individuals engage in conspicuous consumption to signaltheir income to their own reference groups, defined in a finemanner by observable identifiers such as race, gender, education,and occupation. The more income inequality within a refer-ence group, the less prior information concerning the incomeof an individual, and hence the more effective the conspicuousconsumption signal. Therefore, within-group income inequalitycauses substitution from non-conspicuous consumption to con-spicuous consumption. We find strong evidence supporting thisprediction regarding aggregate conspicuous consumption for allincome percentiles. Disaggregating into smaller consumptioncategories, most consumption items categorized by the previ-ous literature as conspicuous and non-conspicuous using surveymethods agrees with this prediction as well.

∗Shanghai University of Finance and Economics. Email: lili@mail.shufe.edu.cn†Shanghai University of Finance and Economics. Email: eric@mail.shufe.edu.cn.‡Arizona State University. Email: Margarita.Pivovarova@asu.edu§We thank Shouyong Shi, Kenneth Burdett and Benoit Julien for their advice and

support. This paper was discussed in the Summer Workshops on Money, Banking,Payments and Finance held in Federal Reserve Bank of St. Louis and Chicago.

1

1 Introduction

Rather than consuming directly for one’s well-being, people mayconsume to influence the public perception of their well-being instead.This second kind of consumption, known as conspicuous consumption,serves to signal for status — through conspicuous consumption, onecan reveal himself as having high income to the public. Conspicuousconsumption, as a means of signaling rather than just for its intrinsicvalue, can crowd out non-conspicuous consumption, sometimes toan extreme that draws the attention of many economists. This paperstudies the substitution between these two kinds of consumption, andrelates that to income inequality within one’s reference group, definedby observables such as occupation, race, gender, age, and educationlevel.

This substitution effect applies to reference groups at all incomelevels. Consider two featuring examples. One reference group of inter-est consists of farmers in the developing countries, who spend 10%of their annual budget on festivals (Banerjee and Duflo, 2007).1 Moti-vated by this finding, Neeman et al. (2012) constructs a conspicuousconsumption model in which the poor signals their wealth throughconspicuous consumption. Whereas the rich is the original focus ofthe conspicuous consumption literature founded by Veblen (1899). Asanother featuring reference group, NFL players are reported to spendconspicuously during their career, yet they file bankruptcies soon afterretirement.2

1Banerjee and Duflo (2007) reports:

Yet the average person living at under $1 per day does not seem toput every available penny into buying more calories. Among our 13countries, food typically represents from 56 to 78 percent among ruralhouseholds, and 56 to 74 percent in urban areas. For the rural poorin Mexico, slightly less than half the budget (49.6 percent) allocatedto purchase food. (...) Perhaps more surprisingly, it is apparent thatspending on festivals is an important part of the budget for manyextremely poor households. (...) The median household spent 10percent of its annual budget on festivals.

2Carlson et al. (2015) reports,

A career lasting 6 years (the median length) will provide an NFL playerwith more earnings than an average college graduate will get in an

2

These two reference groups, which we take as leading examples,are clearly distinct by occupation — knowing a person being an NFLplayer easily distinguish him from a farmer in a developing country.More generally, the public would use observable group identifiersas predictors of an individual’s income, before using conspicuousconsumption as an indirect means of inference. This conditioning,though, do not explain all the aggregate income inequality in earningsregressions; a significant portion of the variation in income is within-group. A large macro literature reports on the wage dispersion amongobservationally homogeneous workers (Hall and Mueller, 2017).3

In this paper, we claim that within-group income inequality isrelated to conspicuous consumption. To this end, we build and test asimple model of conspicuous consumption that hinges on a straight-forward application of Bayes’ theorem. In this model, the public infersan agent’s income by first conditioning on observables that defineshis reference group; this prior, as the within-group income inequality,is non-degenerate. As Bayes’ theorem dictates, the public spread itsupdating weights on the prior and a conspicuous consumption signalsent by the agent.

Suppose that the income inequality within his reference groupincreases; now it becomes harder to determine his income a prioribecause of a more diffused prior. Being less informed, the publicputs a higher weight on the conspicuous consumption signal. Hisconspicuous consumption, with increased influence to the publicinference process, would increase in the expense of non-conspicuousconsumption.

We then extend this analysis to include dynamics. Even in a worldwithout capital markets, conspicuous consumption establishes an

entire lifetime, plus a modest pension. However, earnings are riskybecause an injury can cut a player’s career short. (...) Indeed, we findthat initial bankruptcy filings begin to occur very soon after retirementand continue at a substantial rate through at least the first 12 years ofretirement (Carlson et al., 2015).

3For our two reference group examples, harvest income is idiosyncratic amongfarmers, partly due their low mobility causing difficulties in avoiding geographicrisks such as bad weather (Munshi and Rosenzweig, 2006, 2009); while the incomedistribution of NFL players is highly skewed due to the presence of superstars(Rosen, 1981).

3

intertemporal link because signaling for status today also have effectson future inferences, in case income is persistent. The cumulativesignaling effects leads to more conspicuous consumption relative tothe i.i.d. case.

In our empirical exercise, we examine this implication by compar-ing across reference groups, which differ in within-group income in-equality. We discover that conspicuous consumption and within-groupinequality are positively related for all permanent income percentiles;the reverse conclusion holds true for non-conspicuous consumption.In making this comparison, we control for mean permanent incomeof the group, in order to hold the average purchasing power within areference group constant.

Some confounding factors may undermine the validity of this com-parison. First, reference groups may have heterogeneous preferences— some groups may particularly prefer certain goods that economistsregard as conspicuous consumption, such as clothing and jewelry,without an intention of being conspicuous. Second, reference groupsmay also have different persistence in income, which we have shownto affect the demand for conspicuous consumption. To address theseidentification concerns, we divide the references groups further byyear to obtain a short panel of groups; using this panel, we performthe same exercise controlling for group and year fixed effects, andthe results still hold. The identifying assumption is that preferencesand persistence are time-invariant, while price changes over time arecommon across the reference groups, and thus being absorbed by thetime trend.

We make four remarks about our main result. First, based on ourtheory, we define reference groups using a vector of characteristicstypically considered in wage regressions. We arrive at a large numberof reference groups relative to the existing literature, which focus onprescribed single criterion such as race (Charles et al., 2009; Kaus,2013) or gender (Griskevicius et al., 2007).

Second, according to the permanent income hypothesis (PIH),consumption should depend on permanent income, while in cross-sectional data permanent income is hard to directly identify. If PIHholds, then the total current expenditure of each period should beequal to permanent income. Following Charles et al. (2009), we proxypermanent income by current total expenditure. This proxying implies

4

that both mean permanent income and within-group inequality aremeasured with error. Under a classical measurement error assumption,the resulting attenuation bias would drive the estimated correlationstowards zero. Since our tests are to reject the null of zero correlation,the attenuation bias results in a more stringent test.4

Third, our main result is established using aggregate conspicuousconsumption defined by Charles et al. (2009). As an extension, weevaluate whether each of the consumption items used by Charles et al.(2009) shows their expected correlations, i.e. positive for conspicuousconsumption, negative for non-conspicuous consumption. We findthat the correlation coefficient for most consumption items have theirrespective expected signs, even though there are partial exceptions.Among non-conspicuous items in Charles et al. (2009), food, rent,utility and health show negative correlations as expected; however,entertainment is shown to be conspicuous for all income percentiles,whereas travel is conspicuous only for the rich. Among conspicuousitems in Charles et al. (2009), while cars has positive correlations asexpected, clothing and personal care occupy insignificant consumptionshares; consequently, they show almost zero correlations with incomeinequality. On the whole, our prediction is consistent with the survey-based categorization.

Fourth, we repeat the exercise using data from Vietnam, a devel-oping country, to corroborate our findings. The consumption patternof Vietnamese are different from that of people of the United States,whom the main sample is drawn from. The mean level of income andother group-defining characteristics are also different. Nonetheless,we do observe a similar conclusion.

2 Literature Review

The modern literature on conspicuous consumption formalizes thearguments exposited in Veblen (1899)’s theory of the social class, whichdefines conspicuous consumption as the consumption for status. Inmost models of consumption, the utility function depends directly

4Identifying the true causal effect of income inequality requires searching forexogeneous instruments for both mean permanent income and within-group incomeinequality, which are hard to come by; this important task is left for future exercises.

5

on the amount of consumption. Conspicuous consumption modelsdepart from the standard model by including social status as part ofthe utility function. Specifically, social status refers to how the societyregard the well-being of an individual.

Ireland (1994); Bagwell and Bernheim (1996) build the canonicalmodel of conspicuous consumption.5 This canonical model is an ap-plication of signaling models to the consumption context. The richhave an incentive to reveal themselves as rich using conspicuous con-sumption as a signal, distinguishing thsemelves from the poor. LikeSpence (1973)’s classical signaling model on education, the result is aseparating equilibrium — the rich spends sufficiently much on conspic-uous consumption until the poor cannot follow suit; whereas the poorwould optimally give up altogether in engaging in conspicuous con-sumption, since an insufficient amount of conspicuous consumptioncannot alter the public inference.

Notably, in a separating equilibrium the inference process is de-generate, since the types are fully revealed; the public completelydisregard the prior distribution on the types. Whereas in our model,conspicuous consumption sends a noisy signal of income to the public— it would be difficult to quickly access the value of a luxury good bymerely observing it. As the noise mingles the signals, the public nolonger completely disregard the prior. Hence within-group incomeinequality, as the prior, matters.

The theoretical literature considers a number of issues regard-ing conspicuous consumption which we abstract from. Bagwell andBernheim (1996) consider a general equilibrium model and study theconditions for the existence of Veblen effects. They also show that theequilibrium is inefficient. Neeman et al. (2012) consider an overlap-ping generation model with human capital investment, proving thatconspicuous consumption can lead to a poverty trap.

Charles et al. (2009), in their study of conspicuous consumptionby race, mention that between-race heterogeneity in preferences canexplain any between-race difference in consumption levels, but theresulting theory is tautological. Instead, they abstract from preferencesand emphasize differences in income instead. They find that a Blackperson has a less incentive to engage in conspicuous consumption than

5See also Cole et al. (1992, 1995); Glazer and Konrad (1996).

6

a White person with comparable income. To explain this fact, theypropose that people in each race signals within their own referencegroup. Since Blacks are poorer than Whites on average, a Black person,being relatively rich within his group, would signal more; whereasa comparable White person, being relatively poor within his group,would signal less. Kaus (2013) performs a similar exercise using datafrom South Africa. Our paper is related to theirs by extending theanalysis to many finely defined reference groups instead of two.

Conspicuous consumption are often considered as irrational, whichinvites lack of self-control as another candidate explanation of the samephenomenon. For instance, Carlson et al. (2015) appeal to the lack ofself-control to explain why the NFL players do not save during theircareer. Most self-control models consider a single consumption good,thus abstracting from the concern of substitution between conspicu-ous and non-conspicuous goods. As a notable exception, Banerjeeand Mullainathan (2010) consider a theoretical model in which theydefine temptation goods as those which generate positive utility tothe self which consumes the good, but not to the previous selves thatanticipates the consumption.

3 The Model

3.1 Static Case

For simplicity, we first consider a static economy. There is a continuumof agents indexed by i ∈ I . Agent i’s income is an endowment yi ∈ R+,being log-normally i.i.d. distributed such that log(yi) ∼ N(my, 1/hy),where hy > 0 is a precision parameter (the inverse of variance). Thepublic does not know the realization of yi but only its distribution.

For a particular agent i, ci ∈ R+ is his non-conspicuous (ordinary)consumption, and vi is his conspicuous consumption. Conspicuousconsumption vi ∈ R+ does not enter the utility function directly, sothat it has no intrinsic consumption value; it can be used to manipulatehis status si ∈ R+ according to an updating rule S : R+ → R suchthat si = S(vi). The status, as we shall specify later, represents thepublic posterior mean of agent i’s income. Shutting down the intrinsicvalue of conspicuous consumption vi is not necessary but rather for

7

exposition; we highlight that even in this case, the demand for statusimplies a strictly positive value of conspicuous consumption.

Agent i’s utility is quasi-linear in non-conspicuous consumption:

U(ci, vi) ≡ log ci + bS(vi) (1)

This functional form is assumed for obtaining a closed-form solution.Denote the prices of (ci, vi) by (pc, pv) ∈ R

2+. The budget set of the

agent is B(yi) = {(c, v) ∈ R2+|pcc + pvv ≤ yi}. Given {pc, pv, yi, S},

agent i solves the following utility maximization problem:

max(ci,vi)∈B(yi)

U(ci, vi) (2)

which yields policy functions rc(yi), rv(yi) for ci, vi respectively.The updating rule S is to be determined in the equilibrium. The

public observes a noisy signal of log conspicuous consumption ofagent i:

qi = log vi + εi (3)

where εi ∼ i.i.d.N(0, 1/hε) is a noise term, known to the agent but notto the public; the agent has no control over εi. The public knows agenti’s policy function of vi, and hence qi is indirectly a function of yi —to the public, observing qi is informative on yi. On the other hand,non-conspicuous consumption ci is not observable to the public.

Given the assumed functional forms, there is a simple solution tothis problem. Assume that the updating rule S takes a form of:

S(v) = s0 log(v); s0 ∈ R (4)

In this case, the policy functions are linear in y as rc(yi) = rcyi, rv(yi) =rvyi, where rc = 1/[pc(1 + bs0)], rv = bs1/[pv(1 + bs0)].

In the equilibrium, the public would first adjust the signal on logconspicuous consumption by an amount of − log rv, such that theadjusted signal is the log income plus noise qi = log(yi) + εi. Thenthe public uses Bayes’ rule to determine agent i’s status, which takesthe form of an weighted average of its prior mean and the adjustedsignal as:

si ≡ myφ + qi(1 − φ) (5)

8

where φ ∈ [0, 1] is the updating weight put on the prior mean my, and1 − φ is the updating weight put on the adjusted signal. According toBayes’ rule,

φ =hy

hy + hε(6)

so that the weight on the prior depends on the relative precision ofthe prior and the signal.

Taking this updating rule as given, for agent i his marginal effectof signal manipulation using conspicuous consumption is:

∂si

∂vi=

∂si

∂qi

∂qi

∂vi=

1 − φ

v(7)

which agrees with the assumed log functional form of the updating

rule S, with s0 = 1 − φ. This implies that rc =1

1+b(1−φ), rv = b(1−φ)

1+b(1−φ).

Our model includes that of noiseless signaling as a special case,such that hε = ∞, φ = 0, and that rc = 1/(1 + b), rv = b/(1 + b).In this special case, the prior is completely discarded in Bayesianupdating; consequently, within-group income inequality hy has zeroimpact on conspicuous consumption. Hence for our theory to hold,the signaling noise is key.

Whereas the opposite case is that hε = 0 such that the raw signalis pure noise, then φ = 1 and rc = 1, rv = 0; in this case whereconspicuous consumption cannot be valued by the public, then therecan be no conspicuous consumption.6

It is straightforward to obtain the following comparative statics:

Proposition 1 (Comparative Statics). ∂rc/∂hε < 0, ∂rv/∂hε > 0, ∂rc/∂hy >

0, ∂rv/∂hy < 0, ∂rc/∂b < 0, ∂rv/∂b > 0.

Proposition 1 states that within-group income inequality causessubstitution from non-conspicuous consumption to conspicuous con-sumption. Specifically, consider two groups A and B with the samegroup mean income myA = myB, but Group A has a larger within-group inequality relative to Group B such that hyA < hyB. Proposition

6Certainly, if the conspicuous good has intrinsic value, then its consumption isstill positive.

9

1 would imply that Group A will spend more on conspicuous con-sumption relative to Group B. This is the main proposition that weare going to test.

3.2 Multiple Goods Model

It is straightforward to generalize the above to consider multiplegoods. Now goods are indexed by j ∈ J ≡ {1, 2, . . . , J}, and denote

the vector of all goods of agent i as ci ∈ RJ+. Let the vector of prices

be p ∈ RJ+. The budget set is B(yi) ≡ {c ∈ R

J+|p

′c ≤ yi}. Each goodagent i consumes has a different signaling noise; we denote the vectorby εi ∈ R

J ; we assume that εi ∼ N(0, E) where E ≡ diag(1/h) is adiagonal matrix to impose independence across goods. Utility is givenby:

U(ci) ≡ ∑j∈J

aj log(cij) + bS(ci) (8)

where S : RJ+ → R is the updating rule that depends on the consump-

tion of all goods, which we assume the following form:

S(c) = ∑j∈J

sj log(cj); sj ∈ R+, ∀j ∈ J (9)

The first-order conditions for cij for a particular good j ∈ J is:

aj + bsj

c= λpj (10)

so that c∗ij = rjyi, where rj = (aj + bsj)/[pj ∑j′∈J (aj′ + bsj′)].

The public receives the signals qi = log(ci) + εi = r + log(yi)1+ εi,

where r = (r1, r2, . . . , rJ) ∈ RJ+. The adjusted signals are: qi = qi − r.

Since the signals are independent, Bayes’ rule imply that:

sit = φ0my + ∑j∈J

φjqij (11)

where

φ0 =hy

hy + ∑j∈J hj; φj =

hj

hy + ∑j∈J hj, ∀j ∈ J (12)

10

Using the same reasoning as the two-good case,

pjrj =aj + bφj

∑j′∈J aj′ + bφ′j

(13)

Consider the ratio of two goods A, B ∈ J . Their ratio of consumption

expenditure ispArApBrB

= aA+bφAaB+bφB

and that φA/φB = hA/hB = cφ ∈ R+.

Suppose that good A is a better conspicuous good, such that its ismore observable to the public, with hA > hB such that cφ > 1.

When within-group inequality rises, hy decreases so φA, φB in-creases while maintaining their ratio cφ. Since:

∂

∂φB[aA + bcφφB

aB + bφB] =

b(aBcφ − aA)

(aB + bφB)2(14)

This implies that if two goods have the same intrinsic value such thataA = aB, then the ratio of consumption expenditure increases sincecφ > 1.

3.3 Infinite-Period Model

The one-period model ignores an important concern that, if learn-ing is allowed for multiple periods, then eventually the income ofthe agent will become perfectly known to the public; therefore, it isnot possible to sustain conspicuous consumption at the steady state,even in the presence of a non-degenerate cross-sectional within-groupheterogeneity. This observation is shared in Holmstrom (1999) as well.

As the next step, we consider a dynamic extension of the baseline inwhich the current income of an agent stochastically evolves over time.We shut down the credit market here so there is no direct intertemporaltrade-off. We show that even in this case, the conspicuous consumptionis non-zero; furthermore, conspicuous consumption can generallyaffect future status when income is persistent. Thus an intertemporallink exists.

At any time t ∈ T where T is the set of integers, agent i’s incomeyit is given by:

yit = Zitηit (15)

11

such that Zit is known and ηit is an log-normally distributed innovationunknown to the public. This innovation follows a log AR(1) processthat starts from the infinite past:

log ηit = ρ log ηit−1 + ξit (16)

where ξit ∼i.i.d. N(0, 1/hξ), ρ ∈ (0, 1) is a persistence parameter.The sequence problem at time t = t∗ is:

maxct∗ ,vt∗

Et[∞

∑t=t∗

βτ[log(ct) + St(vt, vt−1, . . .)]] (17)

where ct∗ ≡ {ct}∞t=t∗ , vt∗ ≡ {vt}∞

t=t∗ ; in every period t, (ct, vt) ∈B(yt) ≡ {(c, v)|pcc + pvv = yt}; β ∈ (0, 1) is the discount factor;prices (pc, pv) are constants.

Although the budget set B(yt) has no intertemporal link, cur-rent status is generally affected by not only the current conspicuousconsumption, but the past conspicuous consumptions as well; theeconomy is assumed to be stationary, and that the sequence of pastconspicuous consumption up to time t∗ is an infinite series.

The updating rule at time t, St, is assumed to take the followingform, which shall be justified:

St(vt, vt−1, . . .) =∞

∑τ=0

sτ log(vt−τ) (18)

The first-order conditions for (ct, vt) for any t ≥ t∗ are:

1

ct= λpc (19)

b ∑∞τ=0 βτst−τ

vt= λ (20)

Which means that the solution is still in the form of c∗i = rcyit, v∗i =rvyit as constant proportions of current income.

As before, the second step is to determine the equilibrium updatingrule. The public constructs the adjusted signal of current income foreach period as:

qit = qit − log rv = log Zit + log νit + εit (21)

12

At time t, agent i’s status depends on the public perception giventhe history of adjusted signals qt

i ≡ {qiτ}t−∞. Because of the AR(1)

structure of innovations, past adjusted signals are informative oncurrent income. Consequently, the status sit is determined by theBayes’ rule according to the following:

sit = log Zit + E[log νit|qti ]

= log Zit + E

[

∞

∑τ=0

ρτξit−τ|qti

]

= log Zit +

∞

∑τ=0

ρτE[ξit−τ|qit−τ]

= log Zit +∞

∑τ=0

ρτ(1 − φ)qit−τ (22)

where

φ =hη

hη + hε

=(1 − ρ2)hξ

(1 − ρ2)hξ + hε(23)

Therefore, we have st−τ = ρτ(1 − φ) for any τ ∈ {0, 1, 2, . . .} and

S′(v) =∑

∞τ=0 βτρτ(1 − φ)

v=

1 − φ

(1 − βρ)v(24)

which is strictly positive. In turn, it implies that

rc =1

pc[1 + b(1 − φ)/(1 − βρ)], rv =

b(1 − φ)/(1 − βρ)

pv[1 + b(1 − φ)/(1 − βρ)](25)

This result implies that conspicuous consumption is more prevalentin reference groups that have a high persistence parameter in theirearnings — these reference groups are typically having random-walklike income paths and are perceived as risky.

If ρ = 0, income is i.i.d., with hη = hξ , φ = hξ/(hξ + hε), and

rv =b(1 − φ)

pv(1 + b(1 − φ))

13

In this case, learning about the income of agent i in one period has noprediction power to his income in another period. This i.i.d. featureprevents the public to fully learn about agent i’s income, and henceconspicuous consumption is effective even in the long run.

If ρ → 1, the income process approaches a random walk. In thiscase, φ → 0 since the within-group income inequality explodes. Inthis case, and

rv →b/(1 − β)

pv[1 + b/(1 − β)]

We plot rv as a function of ρ, setting hξ = hε = 1 = b = pv = 1 tovisualize the relationship for intermediate values of ρ in Figure 1:

Figure 1: Relationship between ρ and rv

We summarize the above in the following proposition

Proposition 2 (Persistence). ∂rv/∂ρ > 0, ∂rc/∂ρ < 0. As the persistenceparameter ρ increases, conspicuous consumption becomes more useful sinceits manipulation effect persists over time. The result is substitution fromnon-conspicuous consumption to conspicuous consumption.

14

4 Data and Empirical Results

4.1 Construction of Reference Groups

Following Charles et al. (2009), we are indebted use their publiclyavailable data set produced using the Consumption Expenditure Sur-vey (CEX) to establish these claims. Hence here we describe only theessentials about the raw data here; the reader is referred to Charleset al. (2009) for details.

[We later supplement it by another data set about farmers in Viet-nam, a developing country. ]

The CEX reports how the Americans consume. Specifically, theCEX provides information on consumer buying habits, incomes, andexpenditures, as well as characteristics of households. The mainadvantage of CEX is its vast number of consumption items. Since theprimary purpose of the CEX is to construct consumption weights forinflation adjustment, the Bureau of Labor Statistics spends significanteffort in guaranteeing its quality.

In constrast, the income measure in CEX is unreliable. Charles et al.(2009) report that 27% of the households have their income missing,and the CEX does not impute missing data. The income distributionobtained from the CEX does not match that of better data sets in thisaspect either, such as the Current Population Survey (CPS).

To address this problem, Charles et al. (2009) proxy permanentincome by total expenditure. The idea is that according to permanentincome hypothesis (or life-cycle hypothesis in a finite horizon setting),a rational household, with perfect self-insurance, should amortize hispresent value of all income equally to guarantee smooth consumptionover all periods. Consequently, the amortized present value —thepermanent income— should be equal to the total expenditure inany period. We follow their approach and use total expenditure toapproximate permanent income.

As discussed in the introduction, we aggregate over householdsand construct reference groups defined by a vector of householdcharacteristics, in order to capture the publicly predictable componentof permanent income. We consider household characteristics that aretypically considered in wage regressions (gender, age, race, education,occupation). Given our fine definition of groups, some groups are

15

unavoidably being too small to construct a reliable estimate of thegroup mean and variance. Therefore we select the groups that areabove 10 observations, which is close to the first quartile in terms ofgroup size.

For each group, we evaluate within-group inequality as its log co-efficient of variation (within-group variance normalized by the mean).

To get a sense of how within-group inequality distributes acrossreference groups, Table 1 sorts the constructed reference groups bypermanent income inequality, and report the average group-definingcharacteristics (gender, age, race, education) for each inequality quar-tile. The young, female have more income inequality on average,while there is no clear pattern with respect to race or education (witha scale of 1-4). The relationship is particularly obvious for gender: the1st inequality quartile consists of almost entirely males, whereas thereverse is true for the 4th inequality quartile.

The reverse relationship holds with respect to permanent income.The richest reference groups are on average older and male-dominated.See Table 2.

Given these opposing correlations, it is unsurprising that withoutproper control of permanent income to keep purchasing power con-stant, conspicuous consumption by age and gender do not have amonotonic relationship. See Table 3.

Within-Group Income Inequality Age Male White Education1st Quartile 61.27 0.95 0.62 2.232nd Quartile 48.11 0.72 0.47 2.333rd Quartile 50.56 0.28 0.54 2.254th Quartile 38.65 0.02 0.49 2.36

Table 1: Group-Defining Characteristics by Inequality Quartile

16

Mean Permanent Income Age Male White Education1st Quartile 37.80 0.02 0.46 2.392nd Quartile 50.78 0.27 0.55 2.173rd Quartile 48.41 0.73 0.50 2.374th Quartile 61.68 0.95 0.61 2.23

Table 2: Group-Defining Characteristics by Permanent Income Quartile

Conspicuous Consumption Share Age Male White Education1st Quartile 43.30 0.06 0.47 2.352nd Quartile 50.61 0.48 0.51 2.333rd Quartile 53.37 0.78 0.58 2.304th Quartile 51.34 0.65 0.56 2.18

Table 3: Group-Defining Characteristics by Conspicuous ConsumptionQuartile

In our main analysis, we first sort our reference groups by per-manent income. For each permanent income percentile, we computethe average expenditure shares of conspicuous consumption and non-conspicuous consumption. Figure 2 shows that the expenditure onconspicuous consumption is almost a constant fraction of 8-10% of per-manent income. Notably, the very poor in the United States maintaintheir conspicuous consumption, much like the farmers in developmen-tal countries. Whereas the very rich in the United States, generallyspeaking, are not particularly conspicuous in relative terms.

Next, we match groups by permanent income, and compare matchedgroups whose income inequality and conspicuous consumption differ.Figure 3 plots the conditional correlation of consumption shares andincome inequality (in logs) by permanent income percentile.

To compute the conditional correlation

Corr(C, In|PI)

where C stands for log consumption share, In stands for inequality,and PI stands for permanent income, we first run a regression:

Cg = β0 + β1Ing + β2PIg + β3PIg ∗ Ing + εg (26)

17

0.00

0.25

0.50

0.75

0 25 50 75 100

Permanent Income Percentile

Exp

en

ditu

re S

ha

re

Conspicuous Consumption

Non−Conspicuous Consumption

Figure 2: Consumption Expenditure Shares by Permanent IncomePercentile (United States)

where g is the group subscript. Given this model,

Corr(C, In|PI) =(β1 + β3PI)Var(In|PI)

sd(C|PI)sd(In|PI)(27)

We then find Var(C|PI) and Var(In|PI) by separately regressing C, Inon PI, obtaining and squaring the residuals, and regress the squaredresiduals on PI again. Finally we take square roots to estimate thestandard error terms.

As Figure 3 shows, for all percentiles, conspicuous consumptionis positively correlated to income inequality while non-conspicuousconsumption is negatively correlated to income inequality, agreeingwith our hypothesis.

18

−0.2

−0.1

0.0

0 25 50 75 100

Permanent Income Percentile

Co

rre

latio

n C

oe

ffic

ien

t

Conspicuous Consumption

Non−Conspicuous Consumption

Figure 3: Correlation Coefficients of Log Consumption Shares andInequality by Permanent Income Percentile (United States)

4.2 Controlling for Heterogeneity

To control for heterogeneous preferences across groups, time-seriesvariation is needed. Hence we introduce year as a new group-definingcriterion. The result is a panel of groups where each gender ∗ race ∗age ∗ education reference group has repeated observations by year.We then run the following OLS regression:

Cgt = β0 + β1Ingt + β2PIgt + µg + λt + εgt (28)

where µg, λt are group and year fixed effects, respectively. Since boththe dependent variable and independent variables are in logs, theinterpretations of the regression coefficients are in terms of percentagechanges.

Table 4 shows the regressions of log consumption expenditureshares on inequality and mean permanent income. For interpretation,we normalize both the log consumption shares Cgt and inequality Ingt

to Z-scores, with mean zero and variance 1.In the second and third columns, we partial out the group and year

fixed effects, in order to control for preference heterogeneity and yearlymacroeconomic fluctuations (including changes in relative prices). Fornon-conspicuous consumption, the regression coefficients are negative;

19

for conspicuous consumption, the regression coefficients are positive.Once full controls are introduced, the regression coefficients magnifiedin their respective directions.

The fourth column introduces interaction between inequality andpermanent income, which corresponds to the correlation figure above.When permanent income is below mean (Z-score being negative), theconditional correlation for conspicuous consumption increases, thusproving that conspicuous consumption is particularly relevant for therelatively poor groups, consistent with the correlation by percentilegraph.

Dependent variable:

Conspicuous Consumption (Log Share, Z-score)

(1) (2) (3)

Inequality (Z-score) 0.325∗∗∗ (0.052) 0.179∗∗∗ (0.042) 0.160∗∗∗ (0.042)Mean (Z-score) 0.799∗∗∗ (0.052) 0.822∗∗∗ (0.048) 0.825∗∗∗ (0.048)Interaction −0.057∗∗∗ (0.013)

Group-Defining Dummies No Yes YesYear Dummies No Yes YesObservations 3,020 3,020 3,020R2 0.249 0.720 0.722

Dependent variable:

Non-Conspicuous Consumption (Log Share, Z-score)

(1) (2) (3)

Inequality (Z-score) −0.567∗∗∗ (0.055) −0.421∗∗∗ (0.057) −0.386∗∗∗ (0.057)Mean (Z-score) −0.890∗∗∗ (0.055) −1.230∗∗∗ (0.064) −1.230∗∗∗ (0.064)Interaction 0.104∗∗∗ (0.017)

Group Dummies No Yes YesYear Dummies No Yes YesObservations 3,020 3,020 3,020R2 0.152 0.491 0.498Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

Table 4: OLS of Log Consumption Shares on Within-Group Moments(United States)

20

5 Categorizing Conspicuous Items

According to the categorization by of consumption items by Charleset al. (2009), non-conspicuous consumption is responsible for about80% of all expenditure. While conspicuous consumption has personalcare, clothing and car expenditures as sub-items.

In Charles et al. (2009), the survey question is in the form of:

Consider a person who lives in a household and commu-nity roughly similar to yours. How closely would youhave to interact with this person in order to observe thatthey consistently spend more than average on each of thefollowing consumption categories?

Hence by construction, the answer would depend on the communityin which the respondent lives in, who are the graduate students inUniversity of Chicagos Harris School and Graduate School of Business.

We further investigate if our model holds for each of these items.We plot their expenditure shares in Figure 4. Food expenditure fallsalong the percentiles. Whereas rent, utility and entertainment hasroughly constant expenditure shares. Notably, health expenditure isvery low (less than 5%), because health expenses are idiosyncratic;most individuals has zero expenses during the month of interview.After within-group averaging, the group means would be small.

In contrast, conspicuous consumption items is a much smaller cate-gory. For upper percentiles, car-related expenditure become dominant.We plot their expenditure shares in Figure 5.

Then we compute the conditional correlations by permanent in-come percentile for each of these items. The results for non-conspicuousitems are shown in Figure 6. Food, rent, utility has negative correla-tions, while entertainment and travel shows unexpected signs. Fur-thermore, entertainment is decreasingly conspicuous, while travel isincreasingly conspicuous.

In Banerjee and Duflo (2007) and Neeman et al. (2012), entertain-ment, that in festivals in particular, is regarded as conspicuous. Asnoted by Banerjee and Duflo (2007) though, there are substantialdifferences in the exact form of entertainment among the rich andpoor:

21

0.0

0.1

0.2

0 25 50 75 100

Permanent Income Percentile

Exp

en

ditu

re S

ha

re Health

Entertainment

Food

Rent

Utility

Travel

Figure 4: Expenditure Shares by Group Mean Expenditure (Non-Conspicuous Items, United States)

0.00

0.02

0.04

0.06

0 25 50 75 100

Permanent Income Percentile

Exp

en

ditu

re S

ha

re

Personal Care

Clothing

Car

Figure 5: Expenditure Shares by Percentile (Conspicuous Items, UnitedStates)

22

The under $1 per day households spend very little on theforms of entertainment that are common in rich countries,such as movies, theater, or video shows. In all 13 of thecountries in our sample, in the month preceding the sur-vey the average extremely poor household spent less than1 percent on any of these forms of entertainment. Thecomparable number for the United States is 5 percent.

−0.4

−0.2

0.0

0.2

0 25 50 75 100

Permanent Income Percentile

Co

rre

latio

n C

oe

ffic

ien

t

Health

Entertainment

Food

Rent

Utility

Travel

Figure 6: Correlation by Percentile (Non-Conspicuous Items, UnitedStates)

For the conspicuous items, we plot the corresponding correlationsin Figure 7.

23

−0.1

0.0

0.1

0.2

0 25 50 75 100

Permanent Income Percentile

Co

rre

latio

n C

oe

ffic

ien

t

Personal Care

Clothing

Car

Figure 7: Correlation by Percentile (Conspicuous Items, United States)

6 Conclusion

This paper studies the relationship between the substitution effectbetween conspicuous and non-conspicuous goods, and examine howit is related to within-group income inequality. As our theory pre-dicts, within-group inequality generates a need for the consumersto signal their income to the public, thereby promoting conspicuousconsumption. This prediction is validated from the CEX data, andthat it also agrees with a popular press notion that some particular oc-cupations with risky income such as being sportstars, tend to involvein conspicuous consumption. Whereas the same conclusion can holdfor relatively poor reference groups such as farmers in developingcountries.

As a take-away message, signaling for status is a last resort whenother means are not available. This theory predicts that if incomebecomes more transparent, then conspicuous consumption woulddecrease. As one instance, the salary of some particular professionals,like economics professors, are essentially known within the referencegroup. The welfare benefit of having public information on incomecan be enormous. As our model shows that even if conspicuousconsumption has no intrinsic value, the equilibrium action is to engagein it; if income becomes observable, then all income can be reallocated

24

to non-conspicuous consumption.Another intervention is to introduce risk sharing. For farmers in

developing countries, their risk is largely idiosyncratic. Establishing arisk sharing agreement between farmers would even out the incomedistribution, thereby reducing conspicuous consumption. Hence al-though risk sharing does not improve the average income of farmers,it helps the poor in terms of their welfare.

References

Bagwell, L. S. and B. D. Bernheim (1996): “Veblen Effects in a Theoryof Conspicuous Consumption,” American Economic Review, 349–373.

Banerjee, A. and S. Mullainathan (2010): “The shape of temptation:Implications for the economic lives of the poor,” Tech. rep., NationalBureau of Economic Research.

Banerjee, A. V. and E. Duflo (2007): “The Economic Lives of thePoor,” The journal of economic perspectives, 21, 141–167.

Carlson, K., J. Kim, A. Lusardi, and C. F. Camerer (2015):“Bankruptcy Rates among NFL Players with Short-Lived IncomeSpikes,” American Economic Review, 105.

Charles, K. K., E. Hurst, and N. Roussanov (2009): “ConspicuousConsumption and Race,” Quarterly Journal of Economics, 124, 425–467.

Cole, H. L., G. J. Mailath, and A. Postlewaite (1992): “SocialNorms, Savings Behavior, and Growth,” Journal of Political economy,1092–1125.

——— (1995): “Incorporating concern for relative wealth into eco-nomic models,” Federal Reserve Bank of Minneapolis Quarterly Review,19, 12–21.

Glazer, A. and K. A. Konrad (1996): “A Signaling Explanation forCharity,” American Economic Review, 1019–1028.

25

Griskevicius, V., J. M. Tybur, J. M. Sundie, R. B. Cialdini, G. F.Miller, and D. T. Kenrick (2007): “Blatant benevolence and con-spicuous consumption: when romantic motives elicit strategic costlysignals.” Journal of personality and social psychology, 93, 85.

Hall, R. E. and A. I. Mueller (2017): “Wage Dispersion and SearchBehavior: The Importance of Non-Wage Job Values,” forthcoming inthe Journal of Political Economy.

Holmstrom, B. (1999): “Managerial Incentive Problems: A DynamicPerspective,” The Review of Economic Studies, 66, 169–182.

Ireland, N. J. (1994): “On Limiting the Market for Status Signals,”Journal of public Economics, 53, 91–110.

Kaus, W. (2013): “Conspicuous consumption and race?: Evidencefrom South Africa,” Journal of Development Economics, 100, 63–73.

Munshi, K. and M. Rosenzweig (2006): “Traditional institutionsmeet the modern world: Caste, gender, and schooling choice in aglobalizing economy,” The American Economic Review, 96, 1225–1252.

——— (2009): “Why is mobility in India so low? Social insurance,inequality, and growth,” Tech. rep., National Bureau of EconomicResearch.

Neeman, Z. et al. (2012): “Saving rates and poverty: the role ofconspicuous consumption and human capital,” The Economic Journal,122, 933–956.

Rosen, S. (1981): “The economics of superstars,” The American economicreview, 71, 845–858.

Spence, M. (1973): “Job market signaling,” The quarterly journal ofEconomics, 355–374.

Veblen, T. (1899): The theory of the Leisure Class; An Economic Study ofInstitutions, Random House.

26